Question

The total number of terms in the expansion of $(x+a{)}^{100}+(x-a{)}^{100}$ after simplification will be

• A. 202
• B. 51
• C. 50
• D. None of these

Answer 1

Answer: (B)

Since, $(a+b{)}^n+(a-b{)}^n$
$=2\left[{}^n{C}_0{a}^n{b}^0+{}^n{C}_2{a}^{n-2}{b}^2+{}^n{C}_4{a}^{n-4}{b}^4+\dots \right]$
$=2($ Sum of terms at odd places ) }
So,$(x+a{)}^{100}+(x-a{)}^{100}$
$=2\left({}^{100}{C}_0{x}^{100}{a}^0+{}^{100}{C}_2{x}^{98}{a}^2+\dots .+{}^{100}{C}_{100}{a}^{100}\right)$
$=51$ terms